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Proof step 9 from proof sort-max-last (previous step)

sort(x1 + a ' + x0) = sort(x1 + x0) + a ' ∨ a < max(x1 + x0) ⊦ ins≤(a0, sort(x1 + a ' + x0)) = ins≤(a0, sort(x1 + x0)) + a ', a < max((a0 ' + x1) + x0), a < max(x1 + x0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
sort(x1 + a ' + x0) = sort(x1 + x0) + a ' ⊦ ins≤(a0, sort(x1 + x0) + a ') = ins≤(a0, sort(x1 + x0)) + a ', a < max((a0 ' + x1) + x0), a < max(x1 + x0)

Rule argument

Additional information

Used simplifier rules: ⊦ a ∈ b ' ↔ a = b; (s)% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)% ⊦ a ∈ sort(x) ↔ a ∈ x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list%in-15: ⊦ x + a ' = y → a ∈ y; (forward) from specification list